Bootstrap dependence on plasma profile parameters

The bootstrap fraction, I{sub bs}/I{sub p}, and the shape of the bootstrap current density, J{sub bs}(r), can depend sensitively on the shape of the plasma profiles. Beginning with Hirshman`s form for the bootstrap current density, and making a large aspect ratio expansion (proceeding two orders in the square root of the inverse aspect ratio, {epsilon}), we derive an expression for the bootstrap fraction of the form I{sub bs}/I{sub p} = {epsilon}{sup {1/2}}{beta}{sub p}C{sub bs}({alpha}{sub n}, {alpha}{sub T}; {alpha}{sub J}, {Zeta}, {epsilon}) which depends explicitly on the peakedness of the density, temperature, and current. Examination of contours of constant I{sub bs}/I{sub p} in the space of {alpha}{sub n}, {alpha}{sub T} and consideration of the shape of the bootstrap current density help identify operating regimes for tokamaks which optimize bootstrap current drive.